I am somewhat new to iTunes and how it works when syncing-restoring phones. Seems like I usually have problems with missing apps (recent ones) and restoring music is confusing to me.

But now I have a new problem.

Last week I restored my phone to factory & (upgraded IOS) then restored from a backup (from that same day on my computer) I had some missing apps but I always did so not much of a problem.

My mom came over yesterday and I did the same thing to her phone (first time with her phone on my computer) What I did was authorize this computer, transfer purchases, did a backup to this computer then did a factory restore & upgraded (IOS version) then restored her phone from that backup a made a few minutes ago. It put in her apps & mine. (not paid apps only free apps)

I then restored my phone again yesterday to factory (& upgraded the IOS again) then I did a restore that I created from that day to. It did the same thing it merged our apps (not paid apps) but the free ones. But then I noticed it also switched our Apple id's on our phones.

I then tried to do a different restore to my phone from my computer I created last week (before her phone was ever attached to my computer) and it still has her Apple id on my phone. I even did a restore (from phone) erased everything & setup as a new device and then signed into my Apple id (and it did and was like a new phone) then I went to restore from the backup from last week and it put in her Apple id again.

The iPhone is intented to be connected to one and only one computer -- you cannot move it from one to another without things getting erased and otherwise crossed up. Your mom's iPhone should have been restored on her computer, not yours, or if she had iOS 5 or later she could have updated her iOS over Wi-Fi (no computer needed).

As a corollary to the above, you really can't share apps among devices, unless you're going to always share the same Apple ID for purchases. It doesn't matter if they're free apps, those are associated with an Apple ID. Since your mom probably has her own Apple ID, you can't share apps or any other content from the iTunes store (at least not without some detailed trickery). So, you really can't easily get away with this, and that's really by-design.

If you're missing recent app downloads after you restore, chances are that you have not yet transferred those apps to your computer's iTunes yet and/or you did not perform a backup after downloading the apps. That is probably the explanation, so be sure to sync to iTunes and perform a backup right before restoring your iPhone.

As a corollary to the above, you really can't share apps among devices, unless you're going to always share the same Apple ID for purchases. It doesn't matter if they're free apps, those are associated with an Apple ID. Since your mom probably has her own Apple ID, you can't share apps or any other content from the iTunes store (at least not without some detailed trickery). So, you really can't easily get away with this, and that's really by-design.

Either that's not correct, or I don't understand what you are saying there.

We have three iPhones in the house, all backed up and synced to the same home computer. We all have our own Apple IDs. I have apps on my phone, both free and purchased, that were purchased by Apple IDs other than my own. I know this is the case because from time to time some of the apps that need updating on my phone require me to enter in the password of the purchasing ID - often those are not my ID.

Perhaps this is allowed because all of the IDs are authorized on the home computer.

If you don't have a regular, good backup routine for your music and media you will eventually lose it all.Hint: Using your iPod as your backup strategy is not a good plan.

What I failed to explain clearly is that in the case of an iPhone you can't move them between computers, so sharing apps can't be done like the OP tried to.

I suppose you could use separate computers but share the same Apple ID for re-downloads of prior purchases, but then you're juggling IDs for app updates and new purchases, which doesn't seem worth doing, especially for free apps.